The line bundles on moduli stacks of principal bundles on a curve

TL;DR

This paper determines the structure of the Picard group of moduli stacks of principal G-bundles on smooth projective curves for any affine reductive algebraic group G over an algebraically closed field.

Contribution

It provides a complete description of the Picard group for these moduli stacks, extending previous results to all affine reductive groups and any smooth projective curve.

Findings

Explicit description of the Picard group for principal G-bundles

Extension of known results to all affine reductive groups

Applicable to any smooth projective curve over an algebraically closed field

Abstract

Let G be an affine reductive algebraic group over an algebraically closed field k. We determine the Picard group of the moduli stacks of principal G-bundles on any smooth projective curve over k.